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Simplifying ln(5x + 8) + -1ln(x) = ln(6) Reorder the terms: ln(8 + 5x) + -1ln(x) = ln(6) (8 * ln + 5x * ln) + -1ln(x) = ln(6) (8ln + 5lnx) + -1ln(x) = ln(6) Multiply ln * x 8ln + 5lnx + -1lnx = ln(6) Combine like terms: 5lnx + -1lnx = 4lnx 8ln + 4lnx = ln(6) Reorder the terms for easier multiplication: 8ln + 4lnx = 6ln Solving 8ln + 4lnx = 6ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-6ln' to each side of the equation. 8ln + -6ln + 4lnx = 6ln + -6ln Combine like terms: 8ln + -6ln = 2ln 2ln + 4lnx = 6ln + -6ln Combine like terms: 6ln + -6ln = 0 2ln + 4lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(1 + 2x) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'ln' equal to zero and attempt to solve: Simplifying ln = 0 Solving ln = 0 Move all terms containing l to the left, all other terms to the right. Simplifying ln = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(1 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Add '-2x' to each side of the equation. 2x + -2x = -1 + -2x Combine like terms: 2x + -2x = 0 0 = -1 + -2x Simplifying 0 = -1 + -2x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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